Not sure if this answers your question, but...

If I have a group of tabs I want to save, I just right click on a tab and click 'bookmark all tabs...' then when I want to open that group, I just right click on the folder in my bookmarks and click 'open all in tabs.'

You can do that, but it's too much of a bother. I think it's amazing they screwed up the best features of Firefox with this latest version.

Hi Paul, Thanks for the Booknark all Tip. It is much appreciated. I can now organise my web searching much better now, A problem has created an even better solution! Cheers...

See: https://support.mozilla.com/en-US/kb/Firefox%20does%20not%20ask%20to%20save%20tabs%20and%20windows%20on%20exit?s=open+tabs+from+last+time&as=s

Folks, that solution above from Andy.c is efficient and the right one for me. Restores my previous session WITH my tab groups, which is all I'm interested in. However, FF ppl could think about offering a specific save for tab groups. That would allow launching FF with (all the tabs on) the Home Page and then add one or more specific tab groups (Work - Orchids - Clarinet - ...).

IT'S A EASY AS IT SHOULD BE. This is essentially paulbruster's answer, but I've added the steps some might assume, but which aren't so obvious to those of us who are new at this, like me. This solution might appear to be long and complicated, but after you follow the directions once, you'll find it's quick, clean, and simple. Almost like they designed it this way.

1. If you haven't already, open a bunch of tabs on a few different subjects.
2. Click the List All Tabs button on the right side of the tab strip.
3. Select Tab Groups.
4. Create a few groups as described here , i.e. just drag them out of the main thumbnail group into the new groups they create.
5. Now click on any thumbnail in any new group, but not the original big default group you may have left some tabs in.
6. A regular Firefox window will open, but only the tabs in that group will be visible. You also now have the Tab Groups button in the tab strip.
7. Right click on any tab, and there it is: Bookmark All Tabs. Click on it in the list of options. Or you can hit Ctrl+Shift+D instead and go straight to the dialogue box from the tab without any clicks. But don't go looking for this familiar option anywhere else, 'cause it's not there.
8. Now pick an existing folder or create a new one just like you would have before and shlpam! there they are. New folders are supposed to end up in the Unsorted category all the way at the very bottom, but for some reason mine show up at the bottom of my last sorted category.
9. DO NOT CLICK THE UPPER-RIGHTMOST X to close this group of tabs. This will close ALL of your tabs in all groups, currently visible or not. At least it asks if you're sure first. Instead, click your new Tab Groups button to return to the Boxes 'O Thumbnails window, and click the X in the group box you just bookmarked.
10. Click on another thumbnail to repeat the process with another group, or click on a thumbnail in the big default box to return to the original FF window. You can also click the Tab Groups button at the upper right, or Ctrl+Shift+E, which will also get you into the Boxes 'O Nails window from FF.
11. So now when you reopen FF after shutdown, simply select your folder from your Bookmarks and Open All in Tabs. Just like paulbruster said.